Use Taylor's Theorem to prove that
The Taylor series for the function , centred at a = 0, is given by:
where is the remainder term ( ). To prove that the Taylor series of converges to for all , we must show that the interval of convergence is and .
Coefficients will be for you to find. Use the ratio test to find the interval of convergence.
For the remainder term, notice that:
Use squeeze theorem to finish off (recall: iff )